HI,
I had the same problem as you when I first got my s4. I thought there was a problem with the phone so returned it to no avail. I tried all the BS with the battery monitors and turning everything off etc. I now leave Bluetooth, wifi, gps, screen on high, all the gestures on etc and I still have about 50% by the end of the day.
So, after researching everywhere, I found that the problem was google. It is constantly trying to connect and send location etc. I kid you not, all I did was go to settings>more>location services> and turn off wi fi and mobile network location. THEN go to settings> accounts> google> location settings> turn off.
That was it! I tried this on another friend's phone and it solved his battery issues too. The only catch with this is if you want to use maps, you have to turn it back on.
Let me know if this works for you, I'm curious to know.